I think the answer is no, but maybe I'm missing something: in most repos, you only have one or two admins, and a bunch of "collaborators". But it looks like the collaborators can't assign issues (eg, to themselves), nor can they label issues (even ones they created).
Bug? Design feature? I'm using it wrong? Are there any workarounds?
Looking at Issues 2.0: The Next Generation, this seems to be by design, and from the comments, this isn't the only "problem" users are facing:
One potential workaround (not tested myself) is for a user to fork the original repo, and reproduce the issue in the issue tracker of that new forked repo (that he owns):
Obviously that involves a bit of duplication, but for bugs a user wants complete ownership of, that can be worth doing.